Information processing systems increasingly utilize reconfigurable virtual resources to meet changing user needs in an efficient, flexible and cost-effective manner. For example, cloud computing and storage systems implemented using virtual machines have been widely adopted. Other virtual resources now coming into use in information processing systems include Linux containers. Such containers may be used to provide at least a portion of the virtualization infrastructure of a given information processing system. However, significant challenges arise in deployment of containers in multi-tenant environments. For example, in such environments it can be difficult to isolate storage resources utilized by a container of one tenant from the storage resources utilized by containers of other tenants. As a result, private data of a given tenant container may be exposed to containers of other tenants and to an administrative entity of a corresponding container host device.